 In the adjoining figure, chords AC and BD of a circle with centre | Filo  Class 9

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Circles 535

In the adjoining figure, chords and of a circle with centre , intersect at right angles at . If , calculate .

Solution:
We know that and are the radius

Base angles of an isosceles triangle are equal

So we get

Consider

Using the angle sum property

By substituting the values

On further calculation

By subtraction

So we get

We know that the angle subtended by an arc of a circle at the centre is double the angle subtended by the arc at any point on the circumference

So we get

It can be written as

By substituting the values

By division

So we get

In the

Using the angle sum property

By substituting the values

On further calculation

By subtraction

So we get

Therefore , 535 Connecting you to a tutor in 60 seconds.

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